Adaptive Domain Decomposition method for Saddle Point problem in Matrix Form

Frédéric Nataf (1, 2) , Pierre-Henri Tournier (1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations

We introduce an adaptive domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are the sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods.

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]; Calcul parallèle, distribué et partagé [cs.DC]

Frédéric Nataf, Pierre-Henri Tournier. Adaptive Domain Decomposition method for Saddle Point problem in Matrix Form. 2019. ⟨hal-02343808v3⟩